Vibrating beam force transducers are often used as force-to-frequency converters in accelerometers and other instruments. In one known arrangement, the transducers are used in push-pull pairs in which a given acceleration results in a compression force on one transducer and a tension force on the other transducer. This mode of operation provides a high degree of compensation for many common mode errors, i.e., errors that cause the frequencies of the transducers to shift by the same amount in the same direction, because the shifts cancel in the algorithms normally used to process the transducer outputs. Such errors include vibration rectification errors, errors induced by temperature change, most aging errors, and measurement errors induced by a drift in the clock frequency. To optimize the performance of an accelerometer of this type, it is important for the force transducers to have nearly identical common mode responses.
In recent years, techniques have been developed for fabricating accelerometers from silicon crystals, using micromachining techniques that are similar to those used to create integrated circuits. In an accelerometer to be fabricated using micromachining techniques in silicon, the most straightforward way to create a push-pull accelerometer would be to form one force transducer from the upper surface of the silicon wafer, form the other transducer from the lower surface of the wafer, with the hinge axis of the proof mass positioned somewhere between the transducers. In such an arrangement, rotation of the proof mass about the hinge axis will put one transducer in compression, and the other transducer in tension. The problem with this technique is that the two transducers are formed from different physical layers of the crystal. The two transducers will therefore in general not have well-matched common mode responses.
The problems described above are typical for transducers other than vibrating beam transducers, including surface acoustic wave transducers, metallic strain gauges, and piezoresistive and piezoelectric strain gauges. In some cases, these other transducer types introduce additional common mode problems, such as pyroelectric effects in piezoelectric strain gauges.